延性单晶非均匀变形的三维有限元模拟

对延性单晶在拉伸载荷作用下的应变局域化和颈缩等非均匀变形过程进行了三维有限元数值模拟。将相关晶体塑性本构模型及一种新的数值积分方法补充到ABAQUS6.1商用有限元软件中。该方法的特点是，利用晶体塑性的动力学方程，获得一个关于晶体弹性变形梯度的演化方程，采用半隐式积分方案进行求解。本文推导出一种新的应力变本构矩阵。按此方式更新本构矩阵，计算速度和计算稳定性大大提高。加载方式，边界条件和变形程度等因素影响着滑移系的启动状况，这是平面模型所不能预测的。本文利用三维有限元方法模拟了不同取向下滑移系的启动状况，全面地考虑了FCC单晶材料12个可能滑移系在变形过程中的启动状况，合理地模拟了FCC面心立方单晶沿不同取向加载时晶轴旋转导致的应变局域化和颈缩等非均匀变形过程。

Three Dimensional FEA Simulation of Nonuniform Deformation in Ductile Single Crystals

Nonuniform deformations of ductile single crystals subject to tensile loading are simulated by using three dimensional finite element methods. Rate dependent crystal plasticity model together with a new time integration algorithm has been implemented into ABAQUS6.1 finite element software. The feature of this algorithm is that an evolution equation for the crystal elastic deformation gradient is obtained from crystal kinematics, and an implicit scheme integrates this equation. A new constitutive matrix is presented. It is shown that constitutive matrix updating this way yields significant reduction in computational time. In simulation twelve possible slip systems for FCC single crystals are considered during practical deformations. Nonuniform deformations such as strain localization and necking are simulated rationally and really.